As a transition metal (TM) compound, MnS is also a source of theoretical interest. The electronic structure of TM systems is notoriously challenging to describe and often requires resorting to specialized theories that go beyond the single-particle description.
Thus, MnS, as its oxide counterpart [1]}, is a fruitful and compelling TM system that can be used to test whether or not a single-particle theory such as density functional theory (DFT) [2]}, [3]} can correctly determine its ground-state and other physical properties. Several works have been carried out in that regard using various implementations of DFT [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Although, some studies correctly predicted the AFM-II configuration as the ground-state of RS-MnS, they showed some discrepancy between their predicted local magnetic moment (\(m_{loc}\) ) values of 4.92 \(\mu \) B [7]} and 4.082  \(\mu \) B [9]}, and the neutron diffraction experimental measurement of \(m_{loc} = 4.54\)  \(\mu \) B at \(4.2\)  K [13]}. On the other hand, in order to study the PM phase of MnS, simulations fall into two categories: I) MnS is modeled as a non-magnetic system, i.e., \(m_{loc} = 0\) ; or II) MnS is modeled with finite but randomly oriented local magnetic moments. Investigations employing the non-magnetic approach have the shortcoming that within the single-particle band theory, MnS is always expected to be metallic [6]}, [9]}, since the electron density is uniformly distributed over the orbital states, thus, leading to partially unfilled \(d\) -bands.
The second approach, more compatible with the actual behavior of the Mn local magnetic moments, makes use of the one-electron energy spectrum determined from multiple-scattering theory, namely the Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) method [4]}. Within this picture, non-collinear paramagnetism is achieved when the electron is treated as moving through a medium of completely randomly oriented magnetic moments, then the energy spectrum is obtained by the scattering events that the electron experiences. This scheme, usually called disordered local moments (DLM), is inherently better for modeling PM phases than the non-magnetic approach described above, as it considers an assembly of finite magnetic moments, which corresponds to the experimentally observed PM state of MnS. However, an important drawback of this method, that appears to be critical in the modeling of MnS is that,
the CPA effective potential is constructed in such a way as to represent an average effect of an alloy of randomly oriented moments, therefore, excluding the possibility for individual magnetic moments to develop their own local magnetic environments.
An alternative way to modeling magnetic disorder, and the one employed in this work, is the so-called method of special quasirandom structures (SQS) [17]}. Although collinear by construction, it offers an upper hand over the CPA in that, a SQS is built to represent an average quantity, in this case the net magnetization. This subtle difference
in the dealing with finite magnetic moments with respect to the CPC has been shown to be a source of gapping in TM oxides and perovskites [1]}, [19]}, and we expect it to play an essential role in TM sulphides as well. For a more detailed discussion on the difference between DLM and SQS techniques, see e.g. [1]} and references therein.
